It clicked for me in a narrow entryway in an apartment I rented years ago, the kind with no closet near the door at all, just a wall you walked straight into with your arms full of groceries and a wet umbrella. I put up a coat rack that first week, and suddenly there was one place for everything that used to end up on the back of a chair. It wasn't decorating. It was just a wall finally doing its job.
The thing people get wrong is putting one somewhere it has to compete for attention. A coat rack near a console table loaded with lamps and framed photos just turns into clutter on top of clutter, and a tall freestanding one in a small room reads like a person standing in the corner. Keep it near the door, keep the wall or floor around it fairly plain, and let the coats be the only decoration it's asking for. If you've got a radiator or a heating vent nearby, give it some distance too, nobody wants a damp wool coat steaming an inch from the heat.
If you've never owned one, start simple. A row of wall hooks on a board is the easiest entry point, cheap, quick to put up, and forgiving if you get the spacing slightly wrong the first time, which I did, twice, before I measured properly. A freestanding rack is the next step up, good for renters who can't put holes in a wall, and it has the advantage of moving with you. The elaborate tree shaped ones with a dozen pegs are lovely to look at but only worth it if you actually have a dozen coats living by the door, otherwise you're dusting empty pegs all winter.
Where it earns its place is anywhere coats pile up fast, which in my experience means entryways, mudrooms, the back door everyone actually uses instead of the front one, and any home with kids who shed snow gear like it's a competitive sport. It matters more in fall and winter when there's simply more hanging around, scarves and heavier coats, and less in a mild climate where a light jacket barely needs a hook at all. Apartments benefit as much as big houses, sometimes more, since there's often nowhere else for a coat to go.
The one mistake I'd steer you away from is buying one too small for the household and then being surprised when it's overloaded by November, sagging hooks and all.